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A new method for solving split equality problems via projection dynamical systems

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Abstract

In this paper, we propose a projection dynamical system for solving the split equality problem, or more generally the approximate split equality problem, in Hilbert spaces. The proposed dynamical system endows with the continuous behavior with time for Moudafi’s alternating CQ-algorithm and Byrne and Moudafi’s extended CQ-algorithm. Under mild conditions, we prove that the trajectory of the dynamical system converges weakly to a solution of the approximate split equality problem as time variable t goes to \(+\infty \). We further derive the exponential-type convergence provided that a bounded linear regularity property holds for the approximate split equality problem. Several numerical examples are given to demonstrate the validity and transient behavior of the proposed method.

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Acknowledgments

The authors would like to thank the anonymous referees and the handling editor for their helpful comments and suggestions which have led to the improvement of the early version of this paper.

Funding

This work was partially supported by the National Natural Science Foundation of China (11471230 and 11771067) and the Applied Basic Research Project of Sichuan Province (2018JY0169).

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Authors and Affiliations

  1. College of Mathematics, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Zengzhen Tan & Yaping Fang

  2. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, People’s Republic of China

    Rong Hu

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  1. Zengzhen Tan
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  2. Rong Hu
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  3. Yaping Fang
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Correspondence to Yaping Fang.

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Tan, Z., Hu, R. & Fang, Y. A new method for solving split equality problems via projection dynamical systems. Numer Algor 86, 1705–1719 (2021). https://doi.org/10.1007/s11075-020-00950-5

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